Quantum embedding methods for correlated excited states of point defects: Case studies and challenges

A quantitative description of the excited electronic states point defects and impurities is crucial for understanding materials properties, possible applications in quantum technologies. This a considerable challenge computational methods, since Kohn-Sham density functional theory (DFT) inherently ground-state theory, while higher-level methods are often too computationally expensive defect systems. Recently, embedding approaches have been applied that treat with many-body using DFT to describe bulk host material. We implement such an method, based on Wannierization orbitals constrained random-phase approximation approach, perform systematic characterization method three distinct systems current technological relevance: carbon dimer replacing B N pair hexagonal BN (${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$), negatively charged nitrogen-vacancy center diamond (${\mathrm{NV}}^{\ensuremath{-}}$), Fe impurity Al site wurtzite AlN (${\text{Fe}}_{\text{Al}}$). In context these test-case defects, we demonstrate considerations methodology include convergence screening active-space Coulomb interaction, choice exchange-correlation initial calculation, treatment ``double-counting'' correction. For ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$ show approach gives agreement analytical results Hubbard model, which allows us elucidate effects double-counting ${\mathrm{NV}}^{\ensuremath{-}}$ center, our demonstrates good experiments zero-phonon line triplet-triplet transition. Finally, illustrate challenges associated this determining energies orderings complex spin multiplets ${\text{Fe}}_{\text{Al}}$.